Find the limit.
-$\lim _ { x \rightarrow 1 ^ { - } } \left( \frac { 1 } { x ^ { 4 / 5 } } - \frac { 1 } { ( x - 1 ) ^ { 3 / 5 } } \right)$
A) -$\infty$
B) Does not exist
C) $\infty$
D) 0

Question

Quizplus · Accepted Answer

As $x$ approaches 1 from the left ($1^-$), both denominators in the expression approach 0. However, $x^{4/5}$ approaches 1, while $(x-1)^{3/5}$ approaches 0 more rapidly due to the subtraction inside the parenthesis. This causes the second term to dominate and approach $-\infty$, but since it is subtracted, the overall expression approaches $+\infty$.

Find the Limit lim⁡x→1−(1x4/5−1(x−1)3/5)\lim _ { x \rightarrow 1 ^ { - } } \left( \frac { 1 } { x ^ { 4 / 5 } } - \frac { 1 } { ( x - 1 ) ^ { 3 / 5 } } \right)limx→1−​(x4/51​−(x−1)3/51​)

Find the Limit $\lim _ { x \rightarrow 1 ^ { - } } \left( \frac { 1 } { x ^ { 4 / 5 } } - \frac { 1 } { ( x - 1 ) ^ { 3 / 5 } } \right)$